Title: Around the Numerical Evaluation of D-Finite Functions

Speaker: Dr. Marc Mezzarobba 

Time and place: 28.11.2012, RISC seminar room

Abstract:

D-finite (aka holonomic) functions are the complex analytic solutions of
linear ODEs with polynomial coefficients. The class of D-finite
functions encompasses most elementary functions (exp, ln...) as well as
many common special functions (e.g., Bessel functions and generalized
hypergeometric functions). Its nice algebraic and computational
properties make it possible to develop a unified framework to deal with
these functions in a computer algebra system, instead of developping ad
hoc code for each of them. The DDMF ("Dynamic Dictionary of Mathematical
Functions", http://ddmf.msr-inria.inria.fr/) project aims to put this
idea into practice. The DDMF is an online handbook of special functions
produced automatically starting from a database of mathematical
functions defined by LODE with polynomial coefficients. My talk will
focus on the multiple precision numerical evaluation of D-finite
functions---which takes the place, in the DDMF, of the numerical tables
found in traditional reference works on mathematical functions. I plan
to give an overview on my PhD work on this question, with topics
including fast algorithms for very high precisions and the automatic
computation of tight a priori error bounds.